In case of rain?

I would think that would be fine, if it were me I would definitely do that.

How likely will it rain?

I wouldn't put it in the invite unless there is like 90% chance of rain, which in that case, might as well plan for reception indoor.

Since the indoor location is only a few blocks away, I would just leave it up to chance and if it does rain, leave a big sign up at the original site directing the guests to new site.

My reasoning is that it will most likely confuse some guests to have both locations in the invites.

What if it rain in the morning but clear up in the afternoon? How would the guests know where to go?

We put our rain plan on our website. We also had a "phone tree" set up. If we had to move locations, I would call my mom, dad, MIL, and a designated friend, then they would call their respective families/friends. I made a last-minute poster board sign also. Luckily, we didn't need any of it.

I would put it bc it's very important info if it rains and lots of people don't go on the wedding website